The present invention relates to optical instruments for measuring distance and refractive index. The invention relates in particular to interferometric distance measurement independent of the optical path length effects of refractive index of gas in a measurement path including the effects of refractive index fluctuations.
A frequently-encountered problem in metrology is the measurement of the refractive index of a column of air. Several techniques exist for measuring the index under highly controlled circumstances, such as when the air column is contained in a sample cell and is monitored for temperature, pressure, and physical dimension. See for example, an article entitled xe2x80x9cAn air refractometer for interference length metrology,xe2x80x9d by J. Terrien, Metrologia 1(3), 80-83 (1965).
Perhaps the most difficult measurement related to the refractive index of air is the measurement of refractive index fluctuations over a measurement path of unknown or variable length, with uncontrolled temperature and pressure. Such circumstances arise frequently in geophysical and meteorological surveying, for which the atmosphere is obviously uncontrolled and the refractive index is changing dramatically because of variations in air density and composition. The problem is described in an article entitled xe2x80x9cEffects of the atmospheric phase fluctuation on long-distance measurement,xe2x80x9d by H. Matsumoto and K. Tsukahara, Appl. Opt. 23(19), 3388-3394 (1984), and in an article entitled xe2x80x9cOptical path length fluctuation in the atmosphere,xe2x80x9d by G. N. Gibson et al., Appl. Opt. 23(23), 4383-4389 (1984).
Another example situation is high-precision distance measuring interferometry, such as is employed in micro-lithographic fabrication of integrated circuits. See for example an article entitled xe2x80x9cResidual errors in laser interferometry from air turbulence and nonlinearity,xe2x80x9d by N. Bobroff, Appl. Opt. 26(13), 2676-2682 (1987), and an article entitled xe2x80x9cRecent advances in displacement measuring interferometry,xe2x80x9d also by N. Bobroff, Measurement Science and Tech. 4(9), 907-926 (1993). As noted in the aforementioned cited references, interferometric displacement measurements in air are subject to environmental uncertainties, particularly to changes in air pressure and temperature; to uncertainties in air composition such as resulting from changes in humidity; and to the effects of turbulence in the air. Such factors alter the wavelength of the light used to measure the displacement. Under normal conditions the refractive index of air is approximately 1.0003 with a variation of the order of 1xc3x9710xe2x88x925 to 1xc3x9710xe2x88x924. In many applications the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to 0.003 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and 3 nm, respectively, for a one meter interferometric displacement measurement.
There are frequent references in the art to heterodyne methods of phase estimation, in which the phase varies with time in a controlled way. For example, in a known form of prior-art heterodyne distance-measuring interferometer, the source emits two orthogonally polarized beams having slightly different optical frequencies (e.g. 2 MHz). The interferometric receiver in this case is typically comprised of a linear polarizer and a photodetector to measure a time-varying interference signal. The signal oscillates at the beat frequency and the phase of the signal corresponds to the relative phase difference. A further representative example of the prior art in heterodyne distance-measuring interferometry is taught in commonly-owned U.S. Pat. No. 4,688,940 issued to G. E. Sommargren and M. Schaham (1987). However, these known forms of interferometric metrology are limited by fluctuations in refractive index, and by themselves are unsuited to the next generation of microlithography instruments.
Another known form of interferometer for distance measurement is disclosed in U.S. Pat. No. 4,005,936 entitled xe2x80x9cInterferometric Methods And Apparatus For Measuring Distance To A Surfacexe2x80x9d issued to J. D. Redman and M. R. Wall (1977). The method taught by Redman and Wall consists of employing laser beams of two different wavelengths, each of which is split into two parts. Frequency shifts are introduced into one part of the respective beams. One part of each beam reflects from an object and recombines with the other part on a photodetector. From the interference signal at the detector is derived a phase, at a difference frequency, that is a measure of the distance to the surface. The equivalent wavelength of the phase associated with the difference frequency is equal to the product of the two laser wavelengths divided by the difference of the two wavelengths. This two-wavelength technique of Redman and Wall reduces measurement ambiguities, but is at least as sensitive to the deleterious effects of refractive index fluctuations of the air as single-wavelength techniques.
Another example of a two-wavelength interferometer similar to that of Redman and Wall is disclosed in U.S. Pat. No. 4,907,886 entitled xe2x80x9cMethod And Apparatus For Two-Wavelength Interferometry With Optical Heterodyne Processes And Use For Position Or Range Finding,xe2x80x9d issued to R. Dxc3xa4ndliker and W. Heerburgg (1990). This system is also described in an article entitled xe2x80x9cTwo-Wavelength Laser Interferometry Using Superheterodyne Detection,xe2x80x9d by R. Dxc3xa4ndliker, R. Thalmann, and D. Pronguxc3xa9, Opt. Let. 13(5), 339-341 (1988), and in an article entitled xe2x80x9cHigh-Accuracy Distance Measurements With Multiple-Wavelength Interferometry,xe2x80x9d by R. Dxc3xa4ndliker, K. Hug, J. Politch, and E. Zimmermann. The system of Dxc3xa4ndliker et al., as taught in U.S. Pat. No. 4,907,886, employs laser beams of two wavelengths, each of the beams comprising two polarization components separated in frequency by means of acousto-optic modulation. After passing these beams collinearly through a Michelson interferometer, the polarization components are mixed, resulting in an interference signal, i.e. a heterodyne signal. In that the heterodyne signal has a different frequency for each of the two wavelengths, a so-called superheterodyne signal results therefrom having a frequency equal to the difference in the heterodyne frequencies and a phase associated with an equivalent wavelength equal to the product of the two laser wavelengths divided by the difference of the two wavelengths. According to U.S. Pat. No. 4,907,886 (cited above), the phase of the superheterodyne signal is assumed to be dependent only on the position of a measurement object and the equivalent wavelength. Therefore, this system is also not designed to measure or compensate for the fluctuations in the refractive index of air.
Further examples of the two-wavelength superheterodyne technique developed by Redman and Wall and by Dxc3xa4ndliker and Heerburgg (cited above) are found in an article entitled xe2x80x9cTwo-wavelength double heterodyne interferometry using a matched grating technique,xe2x80x9d by Z. Sodnik, E. Fischer, T. Ittner, and H. J. Tiziani, Appl. Opt. 30(22), 3139-3144 (1991), and in an article entitled xe2x80x9cDiode laser and fiber optics for dual-wavelength heterodyne interferometry,xe2x80x9d by S. Manhart and R. Maurer, SPIE 1319, 214-216 (1990). However, neither one of these examples addresses the problem of refractive index fluctuations.
It may be concluded from the foregoing that the prior art in heterodyne and superheterodyne interferometry does not provide a high speed method and corresponding means for measuring and compensating the optical path length effects of air in a measuring path, particularly effects due to fluctuations in the refractive index of air. This deficiency in the prior art results in significant measurement uncertainty, thus seriously affecting the precision of systems employing such interferometers as found for example in micro-lithographic fabrication of integrated circuits. Future interferometers will necessarily incorporate an inventive, new method and means for measuring and compensating a fluctuating refractive index in a measurement path comprised of a changing physical length.
One way to detect refractive index fluctuations is to measure changes in pressure and temperature along a measurement path and calculate the effect on the optical path length of the measurement path. Mathematical equations for effecting this calculation are disclosed in an article entitled xe2x80x9cThe Refractivity Of Air,xe2x80x9d by F. E. Jones, J. Res. NBS 86(1), 27-32 (1981). An implementation of the technique is described in an article entitled xe2x80x9cHigh-Accuracy Displacement Interferometry In Air,xe2x80x9d by W. T. Estler, Appl. Opt. 24(6), 808-815 (1985). Unfortunately, this technique provides only approximate values, is cumbersome, and corrects only for slow, global fluctuations in air density.
Another, more direct way to detect the effects of a fluctuating refractive index over a measurement path is by multiple-wavelength distance measurement. The basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air. The optical path length is the integrated product of the refractive index and the physical path traversed by a measurement beam. In that the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to determine the physical path length from the optical path length, particularly the contributions of fluctuations in refractive index, provided that the instrument employs at least two wavelengths. The variation of refractive index with wavelength is known in the art as dispersion, therefore this technique will be referred to hereinafter as the dispersion technique.
The dispersion technique for refractive index measurement has a long history, and predates the introduction of the laser. An article entitled xe2x80x9cLong-Path Interferometry Through An Uncontrolled Atmosphere,xe2x80x9d by K. E. Erickson, JOSA 52(7), 781-787 (1962), describes the basic principles and provides an analysis of the feasibility of the technique for geophysical measurements. Additional theoretical proposals are found in an article entitled xe2x80x9cCorrection Of Optical Distance Measurements For The Fluctuating Atmospheric Index Of Refraction,xe2x80x9d by P. L. Bender and J. C. Owens, J. Geo. Res. 70(10), 2461-2462 (1965).
Commercial distance-measuring laser radar based on the dispersion technique for refractive index compensation appeared in the 1970""s. An article entitled xe2x80x9cTwo-Laser Optical Distance-Measuring Instrument That Corrects For The Atmospheric Index Of Refraction,xe2x80x9d by K. B. Earnshaw and E. N. Hernandez, Appl. Opt. 11(4), 749-754 (1972), discloses an instrument employing microwave-modulated HeNe and HeCd lasers for operation over a 5 to 10 km measurement path. Further details of this instrument are found in an article entitled xe2x80x9cField Tests Of A Two-Laser (4416A and 6328A) Optical Distance-Measuring Instrument Correcting For The Atmospheric Index Of Refraction,xe2x80x9d by E. N. Hernandez and K. B. Earnshaw, J. Geo. Res. 77(35), 6994-6998 (1972). Further examples of applications of the dispersion technique are discussed in an article entitled xe2x80x9cDistance Corrections For Single- And Dual-Color Lasers By Ray Tracing,xe2x80x9d by E. Berg and J. A. Carter, J. Geo. Res. 85(B11), 6513-6520 (1980), and in an article entitled xe2x80x9cA Multi-Wavelength Distance-Measuring Instrument For Geophysical Experiments,xe2x80x9d by L. E. Slater and G. R. Huggett, J. Geo. Res. 81(35), 6299-6306 (1976).
Although instrumentation for geophysical measurements typically employs intensity-modulation laser radar, it is understood in the art that optical interference phase detection is more advantageous for shorter distances. In U.S. Pat. No. 3,647,302 issued in 1972 to R. B. Zipin and J. T. Zalusky, entitled xe2x80x9cApparatus For And Method Of Obtaining Precision Dimensional Measurements,xe2x80x9d there is disclosed an interferometric displacement-measuring system employing multiple wavelengths to compensate for variations in ambient conditions such as temperature, pressure, and humidity. The instrument is specifically designed for operation with a movable object, that is, with a variable physical path length. However, the phase-detection means of Zipin and Zalusky is insufficiently accurate for high-precision measurement.
A more modern and detailed example is the system described in an article by Y. Zhu, H. Matsumoto, T. O""ishi, SPIE 1319, Optics in Complex Systems, 538-539 (1990), entitled xe2x80x9cLong-Arm Two-Color Interferometer For Measuring The Change Of Air Refractive Index.xe2x80x9d The system of Zhu et al. employs a 1064 nm wavelength YAG laser and an 632 nm HeNe laser together with quadrature phase detection. Substantially the same instrument is described in Japanese in an earlier article by Zhu et al. entitled xe2x80x9cMeasurement Of Atmospheric Phase And Intensity Turbulence For Long-Path Distance Interferometer,xe2x80x9d Proc. 3rd Meeting On Lightwave Sensing Technology, Appl. Phys. Soc. of Japan, 39 (1989). However, the interferometer of Zhu et al. has insufficient resolution for all applications, e.g. sub-micron interferometry for microlithography.
A recent attempt at high-precision interferometry for microlithography is represented by U.S. Pat. No. 4,948,254 issued to A. Ishida (1990). A similar device is described by Ishida in an article entitled xe2x80x9cTwo Wavelength Displacement-Measuring Interferometer Using Second-Harmonic Light To Eliminate Air-Turbulence-Induced Errors,xe2x80x9d Jpn. J. Appl. Phys. 28(3), L473-475 (1989). In the article, a displacement-measuring interferometer is disclosed which eliminates errors caused by fluctuations in the refractive index by means of two-wavelength dispersion detection. An Ar+ laser source provides both wavelengths simultaneously by means of a frequency-doubling crystal known in the art as BBO. The use of a BBO doubling crystal results in two wavelengths that are fundamentally phase locked, thus greatly improving the stability and accuracy of the refractive index measurement. However, the phase detection means, which employ simple homodyne quadrature detection, are insufficient for high resolution phase measurement. Further, the phase detection and signal processing means are not suitable for dynamic measurements, in which the motion of the object results in rapid variations in phase that are difficult to detect accurately.
In U.S. Pat. No. 5,404,222 entitled xe2x80x9cInterferometric Measuring System With Air Turbulence Compensation,xe2x80x9d issued to S. A. Lis (1995), there is disclosed a two-wavelength interferometer employing the dispersion technique for detecting and compensating refractive index fluctuations. A similar device is described by Lis in an article entitled xe2x80x9cAn Air Turbulence Compensated Interferometer For IC Manufacturing,xe2x80x9d SPIE 2440 (1995). Improvement on U.S. Pat. No. 5,404,222 by S. A. Lis is disclosed in U.S. Pat. No. 5,537,209, issued July 1996. The principal innovation of this system with respect to that taught by Ishida in Jpn. J. Appl. Phys. (cited above) is the addition of a second BBO doubling crystal to improve the precision of the phase detection means. The additional BBO crystal makes it possible to optically interfere two beams having wavelengths that are exactly a factor of two different. The resultant interference has a phase that is directly dependent on the refractive index but is substantially independent of stage motion. However, the system taught by Lis has the disadvantage that it is complicated and requires an additional BBO crystal for every measurement path. In that microlithography stages frequently involve six or more measurement paths, and that BBO can be relatively expensive, the additional crystals are a significant cost burden. An additional disadvantage of Lis"" system is that it employs a low-speed (32-Hz) phase detection system based on the physical displacement of a PZT transducer.
It is clear from the foregoing, that the prior art does not provide a practical, high-speed, high-precision method and corresponding means for measuring refractive index of air and measuring and compensating for the optical path length effects of the air in a measuring path, particularly the effects due to fluctuations in the refractive index of the air. The limitations in the prior art arise principally from the following unresolved technical difficulties: (1) Prior-art heterodyne and superheterodyne interferometers are limited in accuracy by fluctuations in the refractive index of air; (2) Prior-art dispersion techniques for measuring index fluctuations require extremely high accuracy in interference phase measurement, typically exceeding by an order of magnitude the typical accuracy of high-precision distance-measuring interferometers; (3) Obvious modifications to prior-art interferometers to improve phase-measuring accuracy would increase the measurement time to an extent incompatible with the rapidity of stage motion in modern microlithography equipment; (4) Prior-art dispersion techniques require at least two extremely stable laser sources, or a single source emitting multiple, phase-locked wavelengths; (5) Prior-art dispersion techniques in microlithography applications are sensitive to stage motion during the measurement, resulting in systematic errors; and (6) Prior-art dispersion techniques that employ doubling crystals (e.g. U.S. Pat. No. 5,404,222 to Lis) as part of the detection system are expensive and complicated.
These deficiencies in the prior art have led to the absence of any practical interferometric system for performing displacement measurement for microlithography in the presence of a gas in a measurement path where there are typically refractive index fluctuations and the measurement path is comprised of a changing physical length.
Accordingly, it is an object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the refractive index may be fluctuating and/or the physical length of the measurement path may be changing.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the accuracy of measurements and monitoring of the refractive index of the gas and/or of the optical path length effects of the gas are substantially not compromised by a rapid change in physical length of measurement path.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the method and apparatus does not require measurement and monitoring of environmental conditions such as temperature and pressure.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the refractive index of a gas in a measurement path and/or the optical path length effects of the gas wherein the method and apparatus may use but does not require the use of two or more optical beams of differing wavelengths which are phase locked.
It is another object of the invention to provide a method and apparatus for rapidly and accurately measuring and monitoring the optical path length effects of a gas in a measurement path wherein the lengths of measuring paths in an interferometric measurement are substantially not used in a computation of the optical path length effects of the gas.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter. The invention accordingly comprises methods and apparatus possessing the construction, steps, combination of elements, and arrangement of parts exemplified in the detailed description to follow when read in connection with the drawings.
The present invention generally relates to apparatus and methods for measuring and monitoring the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas wherein the refractive index of the gas may be fluctuating, e.g., the gas is turbulent, and/or the physical length of the measuring path may be changing. The present invention also relates to apparatus and methods for use in electro-optical metrology and other applications. More specifically, the invention operates to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path. The refractive index of the gas and/or the optical path length effects of the gas are subsequently computed from the measured dispersion of the refractive index and/or the measured dispersion of the optical path length, respectively. The information generated by the inventive apparatus is particularly suitable for use in interferometric distance measuring instruments (DMI) to compensate for errors related to refractive index of gas in a measurement path brought about by environmental effects and turbulence induced by rapid stage slew rates.
Several embodiments of the invention have been made and these fall broadly into two categories that address the need for more or less precision in final measurements. While the various embodiments share common features, they differ in some details to achieve individual goals.
In general, the inventive apparatus comprises interferometer means having first and second measurement legs at least one of which changes in length and at least one of which is at least in part occupied by the gas. Perferably a reference leg and a measurement leg are used in preferred embodiments. The constituent legs are preferably configured and arranged so that the measurement leg has a portion of its optical path length substantially the same as the optical path length of the reference leg. The gas in the remaining portion of the optical path of the measurement leg in a typical interferometric DMI application is air.
Means for generating at least two light beams having different wavelengths are included. In preferred embodiments, a source generates a set of light beams, the set of light beams being comprised of at least two light beams, each beam of the set of light beams having a different wavelength. The relationship between the wavelengths of the beams of the set of light beams, the approximate relationship, is known.
A set of frequency-shifted light beams is generated from the set of light beams by introducing a frequency difference between two orthogonally polarized components of each beam of the set of light beams such that no two beams of the set of frequency-shifted light beams have the same frequency difference. For a given embodiment, the ratios of the wavelengths are the same as the known approximate relationship to relative precisions which depend on chosen operating wavelenghs and the corresponding known approximate relationship. Because of this wavelength dependence, these relative precisions are referred to as the respective relative precisions of the ratios of the wavelengths. In a number of embodiments, the respective relative precisions of the ratios of the wavelengths are of an order of magnitude less than the respective dispersions of the gas times the relative precision required for the measurement of the respective refractive indices of the gas and/or for the measurement of the respective changes in the optical path length of the measurement leg due to the gas.
In certain ones of the embodiments, the approximate relationship is expressed as a sequence of ratios, each ratio comprising a ratio of low order non-zero integers, e.g., 2/1, to respective relative precisions, the respective relative precisions of the sequence of ratios, wherein a respective relative precision of the respective relative precisions of the sequence of ratios is of an order of magnitude less than the respective dispersion of the gas times the respective relative precision required for the measurement of the respective refractive index of the gas and/or for the measurement of the respective change in the optical path length of the measurement leg due to the gas.
In other embodiments, where the respective relative precisions of the ratios of the wavelengths is inappropriate to the desired value, means are provided for monitoring the ratios of the wavelengths and either providing feedback to control the respective relative precisions of the ratios of the wavelengths, information to correct subsequent calculations influenced by undesirable departures of the respective relative precisions of the ratios of the wavelengths from the desired respective relative precisions of the ratios of the wavelengths, or some combination of both. Means are also provided for monitoring the wavelength used in the primary objective of DMI, the determination of a change in a length of the measurement path.
At least a portion of each of the frequency-shifted light beams is introduced into the interferometer means by suitable optical means so that a first portion of at least a portion of each frequency-shifted light beam travels through the reference leg along predetermined paths of the reference leg and a second portion of at least a portion of each frequency-shifted light beam travels through the measurement leg along predetermined paths of the measurement leg, the first and second portions of at least a portion of each frequency-shifted light beam being different. Afterwards, the first and second portions of at least a portion of each frequency-shifted light beam emerge from the interferometer means as exit beams containing information about the optical path length through the predetermined paths in the reference leg and the optical path length through the predetermined paths in the measurement leg.
Combining means are provided for receiving the exit beams to produce mixed optical signals which contain information corresponding to the phase differences between the exit beams of the first and second portions of at least a portion of each frequency-shifted light beam. The mixed optical signals are then sensed by a photodetector, preferably by photoelectric detection, which operates to generate electrical interference signals that contain information corresponding to the refractive index of the gas at the different beam wavelengths and to the optical path length in the measurement leg due to the refractive index of the gas at the different beam wavelengths.
In certain of the embodiments, modified electrical interference signals are then generated from the electrical interference signals by either multiplying or dividing the phase of each of the electrical interference signals by a number, the relationship of the numbers being either the same as the known approximate relationship of the wavelengths or the same as the reciprocal of the known approximate relationship of the wavelengths, respectively.
The electrical interference signals, or the corresponding modified electrical interference signals depending on the embodiment, are then analyzed by electronic means that operate to determine the dispersion of the optical path length of the measurement leg substantially due to the dispersion of the refractive index of the gas and/or the dispersion (nixe2x88x92nj) of the gas where i and j are integers corresponding to wavelengths and different from one another. From this information and the reciprocal dispersive power of the gas, the refractivity of the gas, (nrxe2x88x921) where r is an integer corresponding to a wavelength, and/or the contribution to the optical path length of the measurement leg due to the refractive index of the gas can also be determined by the electronic means. The value of r may be different from i and j or equal to either i or j. The electronic means can comprise electronic means in the form of a microprocessor or a general purpose computer suitably programmed in well-known ways to perform the needed calculations.
In preferred form, the electrical interference signals comprise heterodyne signals containing phase information corresponding to the refractive index of the gas and to the optical path length of the measurement leg and the apparatus further comprises means to determine the phases of the heterodyne signals to generate phase information corresponding to the dispersion of the refractive index of the gas and to the dispersion of the optical path length of the measurement leg due to the dispersion of the refractive index of the gas. In certain of the embodiments, the apparatus further comprises means for mixing, i.e. multiplying, the modified heterodyne signals corresponding to the modified electrical signals to generate at least one modified superheterodyne signal containing phase corresponding to the dispersion of the refractive index of the gas and to the dispersion of the optical path length of the measurement leg due to the dispersion of the refractive index of the gas. Means are also included for resolving phase ambiguities of the heterodyne signals, modified heterodyne signals, and the modified superheterodyne signals generated in certain of the embodiments. Depending on the details of the optical paths experienced by the light beam portions as they travel through the interferometer means of the various embodiments, additional or different electronics are provided.
While the inventive method disclosed may be carried out using the preferred apparatus described, it will be evident that it may also be practiced using other well-known apparatus. In addition, it is shown that apparatus may be employed which uses homodyne signals.